Bending of Multilayer van der Waals Materials

Abstract

Out-of-plane deformation patterns, such as buckling, wrinkling, scrolling, and folding, formed by multilayer van der Waals materials have recently seen a surge of interest. One crucial parameter governing these deformations is bending rigidity, on which significant controversy still exists despite extensive research for more than a decade. Here, we report direct measurements of bending rigidity of multilayer graphene, molybdenum disulfide (MoS_{2}), and hexagonal boron nitride (hBN) based on pressurized bubbles. By controlling the sample thickness and bubbling deflection, we observe platelike responses of the multilayers and extract both their Young's modulus and bending rigidity following a nonlinear plate theory. The measured Young's moduli show good agreement with those reported in the literature (E_{graphene}>E_{hBN}>E_{MoS_{2}}), but the bending rigidity follows an opposite trend, D_{graphene}<D_{hBN}<D_{MoS_{2}} for multilayers with comparable thickness, in contrast to the classical plate theory, which is attributed to the interlayer shear effect in the van der Waals materials.